Graphing Inverse Functions: Techniques and Practice

This video tutorial focuses on graphing inverse functions. It begins with an introduction to the concept of inverse functions and their graphical representation as reflections across the line y = x. The tutorial provides several examples, demonstrating how to sketch inverse functions and use points to plot them accurately. The video concludes with an advanced example, reinforcing the symmetry and reflection properties of inverse functions.

What line is used as a reference to graph the inverse function?

• x = y

• y = x

• x = -y

• y = -x

How is the inverse function related to the original function graphically?

• It is shifted to the right.

• It is a reflection across the line y = x.

• It is a reflection across the y-axis.

• It is rotated 90 degrees.

What is the significance of the line y = x in graphing inverse functions?

• It determines the slope of the inverse function.

• It is the asymptote of the inverse function.

• It represents the maximum value of the inverse function.

• It acts as a mirror for reflecting the original function.

How do you graph the inverse function of a given function?

• By rotating the graph 180 degrees around the origin.

• By translating the graph upwards.

• By reflecting the graph across the line y = x.

• By stretching the graph vertically.

In the process of graphing an inverse function, what role does the line y = x play?

• It is the axis of symmetry.

• It is the boundary of the function.

• It is the horizontal asymptote.

• It is the vertical asymptote.

When graphing an inverse function using points, what is the first step?

• Switch the x and y coordinates of the points.

• Plot the points of the original function.

• Reflect the points across the y-axis.

• Draw the line y = x.

What ensures that the graph of an inverse function is accurate?

• The points are plotted randomly.

• The points are equally distant from the line y = x.

• The points are equally distant from the y-axis.

• The points are equally distant from the x-axis.

What happens to the coordinates of points when graphing the inverse function?

• The coordinates remain unchanged.

• The x coordinates are squared.

• The y coordinates are halved.

• The x and y coordinates are switched.

What is the relationship between the distances of the original and inverse function from the line y = x?

• They are inversely proportional.

• They are equal.

• There is no relationship.

• They are directly proportional.

Why is it important to plot points accurately when graphing an inverse function?

• To ensure the graph is symmetric about the line y = x.

• To ensure the graph crosses the y-axis at the correct point.

• To avoid running out of space on the graph paper.

• To make the graph look aesthetically pleasing.